Coffee machines of this type are known in a wide variety of embodiments. In EP 0 761 150, for example, this type of coffee machine is described which is provided with an outlet head for the prepared coffee and outlet taps for extracting hot water and steam. In practice, however, multi-functional devices are often asked for which, in addition to coffee, also produce hot and cold milk or milk froth. For this purpose they require two different units, namely one for producing coffee, and the other for producing milk or milk froth. Such devices are structurally complex, and also have relatively high energy consumption due to the separate heating elements for the preparation of the coffee on the one hand and the hot milk and the milk froth on the other hand, especially as in many cases a continuous flow heater is used for this purpose. For this reason they are moreover susceptible to faults because experience has shown that the milk is can easily stick in the pipes of the continuous flow heater.